United goes into its clash with the Gunners looking for a first league win since 3 November as it faces a side sitting eight points above it in the table.
Mourinho was without defenders Victor Lindelof, Chris Smalling and Eric Bailly as United was held to a disappointing 2-2 draw by lowly Southampton on the weekend, and he was asked by MUTV for an update on the injury crisis in defence.
"I don't want to update you," the 55 year-old replied. "I would like Arsenal TV to ask the same questions but they don't, they hide everything from the inside, so why should I answer to you."
Arsenal's visit is the first of two home games in four days for United, which has won only three of its six Premier League fixtures at Old Trafford this season.
The Red Devils entertain Fulham three days later and, with a trip to Liverpool coming off the back of its Champions League game at Valencia on 12 December, Mourinho has made clear the difficulties he faces in picking a balanced XI ahead of such a busy period in the season.
"We are going to be in difficulty again to build the team," he said. "We are again going to have to make adaptations and compensations to try to give some balance to the team.
"But then I believe we are again going to have the spirit to fight and to try to win the match."